Demonstrates boundedness of multidimensional Fourier-Bessel-Hausdorff operators in L_alpha^2 space, highlighting their relationship to wavelet transforms.
In the present paper, we introduce the Hausdorff operators associated with the multidimensional Fourier-Bessel operator ∆α; and we prove the boundedness of the multidimensional Fourier-Bessel-Hausdorff operators on the space L_α^2 ( R_+^d ). We investigate multidimensional Fourier-Bessel wavelet transform, and obtain some useful results. The relation between the multidimensional Fourier-Bessel wavelet transform and multidimensional Fourier-Bessel-Hausdorff operators is also established. The properties of the adjoint multidimensional Fourier-Bessel-Hausdorff operators are further discussed. The results of this paper are illustrated by some examples and figures.
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Soltani et al. (2025) studied this question.
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